ANALYTICAL MECHANICS R = VW+W2
24
and
But since the body is on the point of motion the relation F = /iN holds. Therefore
JL — P cos. ff
: jV~ ^-p sin «'
P
j__~~_______ [f
. DISCUSSION. — (a) When a = 0, R = vP2 + H'"2 and ^ ~ .. (b) When a = jj, # = P - 1^ = 0, therefore P = II7, and ju is imHer-minate. (c) When P = 0, /* = 0, and 22 = TF,
FHK 19.
2. A body which rests upon a rough inclined plane i« brought to tho point of motion up the inclined plane by a horizontal force. Find /* and It. The body is acted upon by three forces, Fig. 19, P, the horizontal force, W, the weight, R, the reaction of the plane.
Replacing R by its components F and N, and taking the axc« along and at right angles to the plane, we obtain
2Z = P cos a — F — W sin a = 0,
™ , 27= -P sina + tf- W cos a = 0.
Therefore
P = P cos a — TF" sin a, # = P sin a + IF cos a,